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Regular version of the site

Article

Quotients of cubic surfaces

European Journal of Mathematics. 2016. Vol. 2. No. 1. P. 333-359.

Let 𝕜 be any field of characteristic zero, X be a cubic surface in ℙ3 and G be a group acting on X. We show that if X(𝕜)≠∅ and G is not trivial and not a group of order 3 acting in a special way then the quotient surface X/G is rational over 𝕜. For the group G of order 3 we construct examples of both rational and nonrational quotients of both rational and nonrational G-minimal cubic surfaces over 𝕜.